Wing Sheung Chan

118 Statistical interpretation and results still primarily limited by statistical uncertainties, as more and more data will be collected in future runs of the LHC and the High-Luminosity LHC, more and more stringent constraints on the LFV Z → `τ decays, or otherwise a discovery, can be expected. 6.4. Combination with existing measurement An observed (expected) upper limit on the Z → µτ branching fraction at 95% CL, B ( Z → µτ ) < 1 . 7(2 . 6) × 10 − 5 , has previously been set using 20 . 3 fb − 1 of √ s = 8 TeV TeV pp collision data collected by ATLAS during the LHC Run 1 [132] . This Run-1 measurement is combined with the measurement in the current analysis to set an even more stringent upper limit on B ( Z → µτ ) . In the Run-1 analysis, the resonant mass m MMC µτ of the µ – τ pair reconstructed using the Missing Mass Calculator [133] was used as the final discriminant for statistical in- terpretations. Four regions were simultaneously fitted to data: two signal regions (SR1 and SR2) binned in m MMC µτ and two one-bin control regions (TCR and WCR) enriched in top-quark and W +jets background events. Same as the current analysis, the parameter of interest was the LFV branching fraction B ( Z → µτ ) . The normalisations of the major backgrounds, Z → τ τ and W +jets, were free floating parameters in the fit. Other minor backgrounds were normalised to their theoretically predicted cross sections. A different data-driven method (the “same-sign method”) was used to estimate fakes instead of the FF method used in the current analysis. The Z → τ τ background was estimated using so-called embedded events, which are observed Z → µµ events where muons are replaced by simulated τ leptons [134] . τ leptons in the signal events are assumed to be unpolarised. The likelihood function for the measurement and the signal and background models were preserved in a RooFit workspace, which makes combination with the current analysis technically possible. When combining the likelihood functions from the two measurements, a correlation scheme is employed where no parameters except the parameters of interest are considered correlated between the two fit models. This decision can be justified by the following reasoning. In both fit models, the parameters of interest carry the same physical meaning as a modifier to B ( Z → `τ ) . They are also both decoupled from σ ( Z ) , A ( Z → `τ → `τ had - vis ) and ε ( Z → `τ → `τ had - vis ) . Moreover, the signal MC samples in both analyses are generated using the same MC generator. Therefore, in the combined fit, the parameters of interest from the two models are set to be 100% correlated. NPs for statistical uncertainties in the two analyses should naturally be uncorrelated, given that the two measurements are based on completely different sets of data. Systematic uncertainties related to the Z → τ τ background estimations are also uncorrelated in the two analyses, given that embedded events were used in the Run-1 analysis while MC generated events are used in the current analysis. Furthermore, both analyses use data- driven methods to estimate fakes and the methods used are very different, implying that